## Tsukuba Journal of Mathematics

### A Maschke type theorem for Hopf $\pi$-comodules

Shuan-hong Wang

#### Abstract

Let $H$ be a Hopf $\pi$-coalgebra and let $A$ be a right group $H$-comodule algebra with a total integral $\phi$. In this article we will find some sufficient conditions under which an epimorphism of $(H, A)$-Hopf $\pi$-comodule splits if it splits $A$-linearly. As an application, we obtain a characterization for an $(H, A)$-Hopf $\pi$-comodule to be projective as an $A$-module, generalizing the one of the Maschke type theorem found in [D2].

#### Article information

Source
Tsukuba J. Math., Volume 28, Number 2 (2004), 377-388.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164806

Digital Object Identifier
doi:10.21099/tkbjm/1496164806

Mathematical Reviews number (MathSciNet)
MR2105942

Zentralblatt MATH identifier
1077.16041

#### Citation

Wang, Shuan-hong. A Maschke type theorem for Hopf $\pi$-comodules. Tsukuba J. Math. 28 (2004), no. 2, 377--388. doi:10.21099/tkbjm/1496164806. https://projecteuclid.org/euclid.tkbjm/1496164806